Lusztig limit of quantum sl(2) at root of unity and fusion of (1,p) Virasoro logarithmic minimal models

We introduce a Kazhdan--Lusztig-dual quantum group for (1,p) Virasoro logarithmic minimal models as the Lusztig limit of the quantum sl(2) at pth root of unity and show that this limit is a Hopf algebra. We calculate tensor products of irreducible and projective representations of the quantum group and show that these tensor products coincide with the fusion of irreducible and logarithmic modules in the (1,p) Virasoro logarithmic minimal models.Comment: 19 page

Breast milk iodine and perchlorate concentrations in lactating Boston-area women

Context: Breastfed infants rely on adequate maternal dietary iodine intake. Objective: Our objective was to measure breast milk iodine and perchlorate, an inhibitor of iodide transport into the thyroid and potentially into breast milk, in Boston-area women. Participants: The study included 57 lactating healthy volunteers in the Boston area. Measurements: Breast milk iodine and perchlorate concentrations and urine iodine, perchlorate, and cotinine concentrations were measured. For comparison, iodine and perchlorate levels in infant formulae were also measured. Results: Median breast milk iodine content in 57 samples was 155 μg/liter (range, 2.7-1968 μg/liter). Median urine iodine was 114 μg/liter (range, 25-920 μg/liter). Perchlorate was detectable in all 49 breast milk samples (range, 1.3-411 μg/liter), all 56 urine samples (range, 0.37-127 μg/liter), and all 17 infant formula samples (range, 0.22-4.1 μg/liter) measured. Breast milk iodine content was significantly correlated with urinary iodine per gram creatinine and urinary cotinine but was not significantly correlated with breast milk or urinary perchlorate. Conclusions: Perchlorate exposure was not significantly correlated with breast milk iodine concentrations. Perchlorate was detectable in infant formula but at lower levels than in breast milk. Forty-seven percent of women sampled may have been providing breast milk with insufficient iodine to meet infants' requirements. Copyright © 2007 by The Endocrine Society

Higher string functions, higher-level Appell functions, and the logarithmic ^sl(2)_k/u(1) CFT model

We generalize the string functions C_{n,r}(tau) associated with the coset ^sl(2)_k/u(1) to higher string functions A_{n,r}(tau) and B_{n,r}(tau) associated with the coset W(k)/u(1) of the W-algebra of the logarithmically extended ^sl(2)_k conformal field model with positive integer k. The higher string functions occur in decomposing W(k) characters with respect to level-k theta and Appell functions and their derivatives (the characters are neither quasiperiodic nor holomorphic, and therefore cannot decompose with respect to only theta-functions). The decomposition coefficients, to be considered ``logarithmic parafermionic characters,'' are given by A_{n,r}(tau), B_{n,r}(tau), C_{n,r}(tau), and by the triplet \mathscr{W}(p)-algebra characters of the (p=k+2,1) logarithmic model. We study the properties of A_{n,r} and B_{n,r}, which nontrivially generalize those of the classic string functions C_{n,r}, and evaluate the modular group representation generated from A_{n,r}(tau) and B_{n,r}(tau); its structure inherits some features of modular transformations of the higher-level Appell functions and the associated transcendental function Phi.Comment: 34 pages, amsart++, times. V2: references added; minor changes; some nonsense in B.3.3. correcte

Lattice fusion rules and logarithmic operator product expansions

The interest in Logarithmic Conformal Field Theories (LCFTs) has been growing over the last few years thanks to recent developments coming from various approaches. A particularly fruitful point of view consists in considering lattice models as regularizations for such quantum field theories. The indecomposability then encountered in the representation theory of the corresponding finite-dimensional associative algebras exactly mimics the Virasoro indecomposable modules expected to arise in the continuum limit. In this paper, we study in detail the so-called Temperley-Lieb (TL) fusion functor introduced in physics by Read and Saleur [Nucl. Phys. B 777, 316 (2007)]. Using quantum group results, we provide rigorous calculations of the fusion of various TL modules. Our results are illustrated by many explicit examples relevant for physics. We discuss how indecomposability arises in the "lattice" fusion and compare the mechanisms involved with similar observations in the corresponding field theory. We also discuss the physical meaning of our lattice fusion rules in terms of indecomposable operator-product expansions of quantum fields.Comment: 54pp, many comments adde

Generalized twisted modules associated to general automorphisms of a vertex operator algebra

We introduce a notion of strongly C^{\times}-graded, or equivalently, C/Z-graded generalized g-twisted V-module associated to an automorphism g, not necessarily of finite order, of a vertex operator algebra. We also introduce a notion of strongly C-graded generalized g-twisted V-module if V admits an additional C-grading compatible with g. Let V=\coprod_{n\in \Z}V_{(n)} be a vertex operator algebra such that V_{(0)}=\C\one and V_{(n)}=0 for n<0 and let u be an element of V of weight 1 such that L(1)u=0. Then the exponential of 2\pi \sqrt{-1} Res_{x} Y(u, x) is an automorphism g_{u} of V. In this case, a strongly C-graded generalized g_{u}-twisted V-module is constructed from a strongly C-graded generalized V-module with a compatible action of g_{u} by modifying the vertex operator map for the generalized V-module using the exponential of the negative-power part of the vertex operator Y(u, x). In particular, we give examples of such generalized twisted modules associated to the exponentials of some screening operators on certain vertex operator algebras related to the triplet W-algebras. An important feature is that we have to work with generalized (twisted) V-modules which are doubly graded by the group C/Z or C and by generalized eigenspaces (not just eigenspaces) for L(0), and the twisted vertex operators in general involve the logarithm of the formal variable.Comment: Final version to appear in Comm. Math. Phys. 38 pages. References on triplet W-algebras added, misprints corrected, and expositions revise

Associative algebraic approach to logarithmic CFT in the bulk: the continuum limit of the gl(1|1) periodic spin chain, Howe duality and the interchiral algebra

We develop in this paper the principles of an associative algebraic approach to bulk logarithmic conformal field theories (LCFTs). We concentrate on the closed $gl(1|1)$ spin-chain and its continuum limit - the $c=-2$ symplectic fermions theory - and rely on two technical companion papers, "Continuum limit and symmetries of the periodic gl(1|1) spin chain" [Nucl. Phys. B 871 (2013) 245-288] and "Bimodule structure in the periodic gl(1|1) spin chain" [Nucl. Phys. B 871 (2013) 289-329]. Our main result is that the algebra of local Hamiltonians, the Jones-Temperley-Lieb algebra JTL_N, goes over in the continuum limit to a bigger algebra than the product of the left and right Virasoro algebras. This algebra, S - which we call interchiral, mixes the left and right moving sectors, and is generated, in the symplectic fermions case, by the additional field $S(z,\bar{z})=S_{ab}\psi^a(z)\bar{\psi}^b(\bar{z})$, with a symmetric form $S_{ab}$ and conformal weights (1,1). We discuss in details how the Hilbert space of the LCFT decomposes onto representations of this algebra, and how this decomposition is related with properties of the finite spin-chain. We show that there is a complete correspondence between algebraic properties of finite periodic spin chains and the continuum limit. An important technical aspect of our analysis involves the fundamental new observation that the action of JTL_N in the $gl(1|1)$ spin chain is in fact isomorphic to an enveloping algebra of a certain Lie algebra, itself a non semi-simple version of $sp(N-2)$. The semi-simple part of JTL_N is represented by $Usp(N-2)$, providing a beautiful example of a classical Howe duality, for which we have a non semi-simple version in the full JTL image represented in the spin-chain. On the continuum side, simple modules over the interchiral algebra S are identified with "fundamental" representations of $sp(\infty)$.Comment: 69 pp., 10 figs, v2: the paper has been substantially modified - new proofs, new refs, new App C with inductive limits construction, et

UV and EUV Instruments

We describe telescopes and instruments that were developed and used for astronomical research in the ultraviolet (UV) and extreme ultraviolet (EUV) regions of the electromagnetic spectrum. The wavelength ranges covered by these bands are not uniquely defined. We use the following convention here: The EUV and UV span the regions ~100-912 and 912-3000 Angstroem respectively. The limitation between both ranges is a natural choice, because the hydrogen Lyman absorption edge is located at 912 Angstroem. At smaller wavelengths, astronomical sources are strongly absorbed by the interstellar medium. It also marks a technical limit, because telescopes and instruments are of different design. In the EUV range, the technology is strongly related to that utilized in X-ray astronomy, while in the UV range the instruments in many cases have their roots in optical astronomy. We will, therefore, describe the UV and EUV instruments in appropriate conciseness and refer to the respective chapters of this volume for more technical details.Comment: To appear in: Landolt-Boernstein, New Series VI/4A, Astronomy, Astrophysics, and Cosmology; Instruments and Methods, ed. J.E. Truemper, Springer-Verlag, Berlin, 201

Launch of the Space experiment PAMELA

PAMELA is a satellite borne experiment designed to study with great accuracy cosmic rays of galactic, solar, and trapped nature in a wide energy range protons: 80 MeV-700 GeV, electrons 50 MeV-400 GeV). Main objective is the study of the antimatter component: antiprotons (80 MeV-190 GeV), positrons (50 MeV-270 GeV) and search for antimatter with a precision of the order of 10^-8). The experiment, housed on board the Russian Resurs-DK1 satellite, was launched on June, 15, 2006 in a 350*600 km orbit with an inclination of 70 degrees. The detector is composed of a series of scintillator counters arranged at the extremities of a permanent magnet spectrometer to provide charge, Time-of-Flight and rigidity information. Lepton/hadron identification is performed by a Silicon-Tungsten calorimeter and a Neutron detector placed at the bottom of the device. An Anticounter system is used offline to reject false triggers coming from the satellite. In self-trigger mode the Calorimeter, the neutron detector and a shower tail catcher are capable of an independent measure of the lepton component up to 2 TeV. In this work we describe the experiment, its scientific objectives and the performance in the first months after launch.Comment: Accepted for publication on Advances in Space Researc

Male partners’ support and influence on pregnant women’s oral PrEP use and adherence in Malawi

Introduction: Daily oral pre-exposure prophylaxis (PrEP) is a safe and effective HIV prevention method for pregnant and postpartum women, but adherence barriers exist. Understanding the role of male partners in supporting PrEP use may inform strategies to support PrEP adherence among pregnant and breastfeeding women. Methods: To understand male partners’ involvement in women's use of PrEP, we conducted in-depth interviews with pregnant women in Lilongwe, Malawi who had recently decided to use PrEP (n = 30) and their male partners (n = 20) in the context of a PrEP adherence trial. Women were purposively recruited to ensure variation in their partners’ HIV status. Interviews were conducted in Chichewa using a semistructured guide. We followed a thematic approach to analyze the interview data. Results: Most male partners were receptive to women using PrEP during pregnancy because it eased their fears of the woman and baby acquiring HIV. Men often played a key role in women's PrEP adherence by providing daily reminders and encouragement to adhere to their medication. The majority of women appreciated this support from the men as it lessened the burden of remembering to take their medications daily on their own and aided their adherence. However, several women who lacked male partner support spoke of wanting their partners to be more involved. Many men living with HIV found the mutual support beneficial for their antiretroviral therapy adherence, while men without HIV or with status unknown appreciated knowing that the family was protected. While most men were open to women continuing PrEP beyond the current study, some would only support it if women were still at risk for acquiring HIV. Conclusion: In this study, male partners were strongly motivated to support the PrEP adherence of their female partners as a way of ensuring that the pregnant women and unborn babies were protected against HIV. Promoting disclosure and tangible support that arises organically among men may be helpful, but programs to enhance this support and identify ways to support women who do not receive support from their partners or do not wish to disclose their PrEP use to partners may be needed. 2023 Young, Saidi, Phanga, Tseka, Bula, Mmodzi, Pearce, Maman, Golin, Mutale, Chi and Hill